1. COSMO 2006, Lake Tahoe 9/28/2006 Cuscuton Cosmology: Cuscuton Cosmology: Dark Energy meets Modified Gravity Niayesh Afshordi Institute for Theory and Computation Harvard College Observatory

2. Niayesh Afshordi COSMO 06 My Collaborators Ghazal Geshnizjani (UW-Madison)Daniel Chung (UW-Madison)Michael Doran (Heidelberg) Afshordi, Chung, & Geshnizjani; hep-th/0609150 Afshordi, Chung, Doran, & Geshnizjani; astro-ph/0610??? Check out her poster today!

3. Niayesh Afshordi COSMO 06 Outline What is Cuscuton? Dark Energy with c s = 1 – Is Cuscuton causal? – Cuscuton: soap bubbles in Minkowski space – An underlying theory for Cuscuton Cuscuton Cosmology: – Dark Energy meets Modified Gravity – Quadratic Cuscuton: Early Dark Energy – Exponential Cuscuton: DGP-like cosmic history Why should we care?

4. Niayesh Afshordi COSMO 06 Take the scalar field action: In the field comoving frame,   = 0; but  P   0  c s = 1 Field equation becomes a constraint equation that uniquely determines as a function of metric  No internal dynamics; only follows what it couples to  Cuscuton (käs-kǖ-tän): derived from the Latin name for the parasitic plant of dodder, “Cuscuta” What is Cuscuton?

5. Niayesh Afshordi COSMO 06 Is Cuscuton Causal? Phase space volume of linear perturbations vanishes in the homogeneous limit  They cannot carry information  Causality will constrain Cuscuton couplings

6. Niayesh Afshordi COSMO 06 Cuscuton as Soap bubbles Field equation yields, where K(  ) is the extrinsic curvature of constant field hypersurfaces  analog of bubbles in Euclidian space

7. Niayesh Afshordi COSMO 06 An underlying theory for Cuscuton Imagine a field theory with discrete degrees of freedom The only local action in the low energy limit (in lieu of other couplings) is the discrete Cuscuton action

8. Niayesh Afshordi COSMO 06 Cuscuton Cosmology Artist’s Conception

9. Niayesh Afshordi COSMO 06 Friedmann Cuscuton Cosmology Field Equation (remember bubbles):  Friedmann equation: (in a flat universe)

10. Niayesh Afshordi COSMO 06 Cuscuton as Modified Gravity Since Cuscuton has no internal dynamics, it can be viewed as a (non-local) modification to gravity Non-locality is exponentially suppressed beyond the Hubble radius, i.e. for k << H, the evolution is local

11. Niayesh Afshordi COSMO 06 More cosmology with Cuscuton Cuscuton is a minimal theory for evolving dark energy, as it has no internal dynamics Examples: Quadratic potential: – Geometry evolves exactly as  CDM – Only differs after fluctuations cross horizon Exponential potential: – Geometry evolves exactly as DGP cosmology

12. Niayesh Afshordi COSMO 06 Quadratic Cuscuton Cosmology + Friedmann eq.   CDM expansion history, but: Early Dark Energy perturbations decayearly ISW effect

13. Niayesh Afshordi COSMO 06 Preliminary constraints on Quadratic Cuscuton Main constraints from ISW effect, i.e. WMAP3  Q < 0.035 (95%)  or  < 0.4 m 1/2 (in Planck units) for the action:

14. Niayesh Afshordi COSMO 06 Exponential (DGP-like) Cuscuton Exact same expansion history as flat DGP self- accelerating model (no difference in geometric tests) But, different sub-horizon perturbation theory – Like quintessence with the same expansion history 5-10% difference with DGP  detectable at < 3  with weak lensing+ext (c.f. Dragan’s talk; Huterer & Linder 06) Song, Sawicki, & Hu 06  DGP and exponential Cuscuton can only be marginally distinguished at low z

15. Niayesh Afshordi COSMO 06 ISW effect: DGP-like Cuscuton vs. DGP Song, Sawicki, & Hu 06 (see next talk!) Due to anisotropic stress (?) DGP gives much larger ISW DGP-like Cuscuton yields only. 5% larger C l ’s than DGP-like quintessence ISW effect can be potentially used to distinguish DGP-like Cuscuton from DGP

16. Niayesh Afshordi COSMO 06 Why should we care? (minimal) Cuscuton is causal is a minimal theory of evolving DE (no internal dynamics) is stable against quantum corrections at low energies (geometric model) blurs the observational distinctions between modified gravity and dark energy models

17. Niayesh Afshordi COSMO 06